Current Reading

This blog is primarily for me to blog my responses to books that I'm reading. Sometimes I blog about other stuff too, though.

I'm currently re-reading Systems of Survival by Jane Jacobs.

Word cloud

Word cloud

Tuesday, July 19, 2016

Principia Book 1, Section 2, Propositions 1-3: Tricky but rewarding

The Principia is almost entirely geometry, not algebra, but it is worth it.  The first proposition in Book 1, Section 2 has the most intuitive diagram ever drawn for explaining centripetal forces.  The proofs for the theorem and corollaries derived from it are a bit of a slog for somebody who hasn't done tons of geometric proofs in forever, but the basic insight into centripetal motion from the diagram itself is perfect.  Also, this very first proposition is equal areas in equal times.  The man does not waste any time, he just gets right into fundamental results, and then his corollaries establish visual interpretations of forces.  Beautiful stuff.

In the second proposition he just shows that if you observe something moving in such a way as to sweep out equal areas in equal times (looking at arcs drawn about some designated center) then it must be acting under a centripetal force.

In the third proposition he argues that if a body is tracing out equal areas in equal times with respect to some accelerating object, then the first body must be under the combined influence of a centripetal force from the second object and also the same accelerative force as the second object is feeling.  In other words, Newton translates his results to non-inertial frames.

So far the man has built laid down basic laws of motion, described a painstaking experiment, built up calculus, derived one of Kepler's Laws, and developed some physics for non-inertial frames.  This is why physicists regard him as something of a deity.  He's blending together a bunch of techniques and fundamental concepts, any one of which could easily be a claim to some fame in the history of physics, and at the same time he's blending together skill sets that few physicists will ever master simultaneously.

This is why we love him.

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